AMC12 2014 B

AMC12 2014 B · Q2

AMC12 2014 B · Q2. It mainly tests Fractions, Arithmetic misc.

Orvin went to the store with just enough money to buy 30 balloons. When he arrived he discovered that the store had a special sale on balloons: buy 1 balloon at the regular price and get a second at $\frac{1}{3}$ off the regular price. What is the greatest number of balloons Orvin could buy?

Orvin 带着刚好够买 30 个气球的钱去商店。到了那里，他发现商店正在搞特价活动：买一个气球按原价，第二个气球打 $\frac{1}{3}$ 折。Orvin 最多能买多少个气球？

(A) 33 33

(B) 34 34

(D) 38 38

(E) 39 39

Answer

Correct choice: (C)

正确答案：（C）

Solution

The special allows Orvin to purchase balloons at $\frac{1 + \frac{2}{3}}{2} = \frac{5}{6}$ times the regular price. Because Orvin had just enough money to purchase 30 balloons at the regular price, he may now purchase $30 \cdot \frac{6}{5} = 36$ balloons.

特价让 Orvin 以 $\frac{1 + \frac{2}{3}}{2} = \frac{5}{6}$ 倍原价购买气球。因为 Orvin 的钱刚好够买 30 个原价气球，现在他能买 $30 \cdot \frac{6}{5} = 36$ 个气球。

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